Opinion

The petitioner, Eric Kennedy, appeals following the denial of his petition for certification to appeal from the judgment of the habeas court denying his amended petition for a writ of habeas corpus1 and claims that the habeas court abused its discretion in denying his petition for certification to appeal. The court concluded that the petitioner had failed to demonstrate that the trial attorney who had represented him on the underlying charges as enumerated in his habeas petition rendered ineffective assistance of counsel by failing (1) to advise him adequately of the consequences of his plea agreement as to the maximum sentence to be imposed and (2) to research adequately the length of sentences imposed in comparable cases charging other defendants with crimes involving “shaken baby syndrome.” We dismiss the appeal.

The following procedural history is relevant to this appeal. The most recent charges brought against the petitioner that are at issue in this appeal were the result *70of a January 8, 2004 incident in which the state charged the petitioner with inflicting head injuries upon his son, a healthy ten month old infant, causing the child to be permanently disabled.2 On September 2, 2005, the petitioner pleaded guilty, pursuant to North Carolina v. Alford, 400 U.S. 25, 37, 91 S. Ct. 160, 27 L. Ed. 2d 162 (1970), to one count of assault in the first degree in violation of General Statutes § 53a-59a (a) (3) and one count of risk of injury to a child in violation of General Statutes § 53-21. The sentencing agreement was for a maximum sentence of twenty-five years incarceration, execution suspended after twenty years, followed by five years probation, with a minimum sentence of twenty years incarceration, execution suspended after fifteen years, followed by five years probation. The trial court sentenced the petitioner to twenty years incarceration, execution suspended after fifteen years, followed by five years of probation for the assault in the first degree conviction, and five years incarceration for the risk of injury to a child conviction to be served consecutively to the sentence imposed on the assault conviction.3 All remaining counts not arising from the January 8, 2004 injury to the petitioner’s son were nolled.

On November 13, 2009, the petitioner filed an amended petition for a writ of habeas corpus, claiming *71that the attorney representing him when he entered his plea agreement, Michael Moscowitz, had provided ineffective assistance of counsel by failing, inter alia: (1) to interview potential exculpatory witnesses, (2) to research and investigate the range of sentences imposed in cases that were similar to the petitioner’s case and (3) to object to or inform the petitioner of the entry of nolles in connection with other pending charges against him that were unrelated to his son’s injuries.4 On March 4, 2010, following a trial on the merits, the habeas court rejected all counts of the petition. The habeas court subsequently denied the petitioner’s petition for certification to appeal.

On appeal to this court, the petitioner claims that the habeas court abused its discretion when it denied his petition for certification to appeal that court’s finding that Moscowitz’ representation during the plea negotiations and entry of the petitioner’s plea agreement was ineffective because (1) he did not inform the petitioner that he would be required to serve between twenty and twenty-five years in prison and (2) he did not adequately research sentences issued in similar cases. We are not persuaded.

“The standard of review for a habeas court’s denial of a petition for certification to appeal requires the petitioner to prove that the denial of the petition for certification was an abuse of discretion and also that *72the decision of the habeas court should be reversed on the merits. ... To prove an abuse of discretion, the petitioner must demonstrate that the resolution of the underlying claim involves issues [that] are debatable among jurists of reason; that a court could resolve the issues [in a different manner]; or that the questions are adequate to deserve encouragement to proceed further. ... In a habeas appeal, this court cannot disturb the underlying facts found by the habeas court unless they are clearly erroneous, but our review of whether the facts as found by the habeas court constituted a violation of the petitioner’s constitutional right to effective assistance of counsel is plenary.” (Internal quotation marks omitted.) Crawley v. Commissioner of Correction, 141 Conn. App. 660, 664, 62 A.3d 1138 (2013).

“[T]he governing legal principles in cases involving claims of ineffective assistance of counsel arising in connection with guilty pleas are set forth in Strickland [v. Washington, 466 U.S. 668, 104 S. Ct. 2062, 80 L. Ed. 2d 674 (1984)] and Hill [v. Lockhart, 474 U.S. 62, 106 S. Ct. 366, 88 L. Ed. 2d 203 (1985)]. [According to] Strickland, [an ineffective assistance of counsel] claim must be supported by evidence establishing that (1) counsel’s representation fell below an objective standard of reasonableness, and (2) counsel’s deficient performance prejudiced the defense because there was a reasonable probability that the outcome of the proceedings would have been different had it not been for the deficient performance. . . . The first prong requires a showing that counsel made errors so serious that counsel was not functioning as the counsel guaranteed . . . by the [s]ixth [a]mendment. . . . Under . . . Hill . . . which . . . modified the prejudice prong of the Strickland test for claims of ineffective assistance when the conviction resulted from a guilty plea, the evidence must demonstrate that there is a reasonable probability that, but for counsel’s errors, [the petitioner] would not *73have pleaded guilty and would have insisted on going to trial. ... In its analysis, a reviewing court may look to the performance prong or to the prejudice prong, and the petitioner’s failure to prove either is fatal to a habeas petition.” (Emphasis in original; internal quotation marks omitted.) Hall v. Commissioner of Correction, 124 Conn. App. 778, 782-83, 6 A.3d 827 (2010), cert. denied, 299 Conn. 928, 12 A.3d 571 (2011).

The petitioner first claims that he would not have pleaded guilty had he known that his plea agreement carried a possible maximum sentence of twenty-five years incarceration, rather than a maximum of ten years. At the habeas trial, the petitioner testified to this effect. Moscowitz, however, testified that he had discussed with the petitioner the plea agreement and the possible sentencing range that the trial court might impose, up to and including a maximum sentence of twenty-five years. Moscowitz also denied that a sentence of ten years incarceration was ever discussed with the petitioner. The habeas court found Moscowitz to be a more credible witness, and determined, on the basis of this and other evidence presented at the habeas trial,5 that the petitioner had been advised adequately concerning the possible sentence accompanying his plea agreement. Thus, the habeas court found that the petitioner’s claim of deficient performance failed due to the habeas court’s credibility determinations. “The habeas judge, as the trier of facts, is the sole arbiter of the credibility of witnesses and the weight to be given their testimony.” (Internal quotation marks omitted.) Josephs v. Commissioner of Correction, 117 Conn. App. *74431, 433, 979 A.2d 568, cert. denied, 294 Conn. 906, 982 A.2d 1080 (2009). Accordingly, because the habeas court determined that Moscowitz’ testimony was credible, we defer to that court’s finding and agree that the petitioner was adequately advised of the possible sentence that might result from his plea agreement.6

The petitioner next claims that Moscowitz’ representation was deficient because he did not adequately research the duration of sentences received by defendants in similar “shaken baby” cases. He argues that, as a result, he pleaded guilty on the basis of Moscowitz’ “gross misadvice” regarding the “likely range of sentences” that he faced. The petitioner, however, fails to demonstrate how such an absence of research on this topic amounted to deficient performance or that he would have changed his pleas on the basis of any such comparison.

Sentencing in Connecticut “is an individualized procedure in which the court has the grave responsibility to determine and impose, within applicable statutory limits, the appropriate punishment for a particular defendant.” (Internal quotation marks omitted.) State v. Fuller, 56 Conn. App. 592, 624, 744 A.2d 931, cert. denied, 252 Conn. 949, 748 A.2d 298, cert. denied, 531 U.S. 911, 121 S. Ct. 262, 148 L. Ed. 2d 190 (2000). It has been well established by both the United States Supreme Court and our Supreme Court that there is no due process liberty interest or other constitutional right to the type of proportionality review that the petitioner claims was required by Moscowitz in this case. See *75Pulley v. Harris, 465 U.S. 37, 43-51, 104 S. Ct. 871, 79 L. Ed. 2d 29 (1984) (proportionality review not constitutional requirement even when death sentence imposed); State v. Rupar, 293 Conn. 489, 504-505, 978 A.2d 502 (2009) (“there can be no liberty interest implicit in the fourteenth amendment [to the United States constitution] in receiving a sentence within the authorized range that is ‘proportionate’ to that of similarly situated offenders”).

Moscowitz, therefore, had no legal obligation to research comparable sentences in similar cases. Moreover, the petitioner has not cited any cases that demonstrate that his sentence was grossly disproportionate in comparison to the sentences of other defendants who were convicted of crimes involving “shaken baby syndrome,”7 nor does he claim that his sentence was actually disproportionate. Thus, we conclude that because Moscowitz’ performance was not deficient in regard to this claim, the habeas court’s conclusion was not in error.

Because we conclude that Moscowitz’ representation was not deficient with respect to the petitioner’s claims, we do not reach the prejudice prong of Strickland, namely, whether but for counsel’s deficient performance the petitioner would not have pleaded guilty, but would have proceeded to trial.8 See Hall v. Commissioner of Correction, supra, 124 Conn. App. 782-83. *76Accordingly, we conclude that the habeas court’s resolution of the issues is not debatable among jurists of reason, that a court could not resolve the issues in a different manner, and that the questions raised do not deserve encouragement to proceed further. See Crawley v. Commissioner of Correction, supra, 141 Conn. App. 664. The habeas court, therefore, did not abuse its discretion in denying the petitioner’s petition for certification to appeal.

The appeal is dismissed.